Breakdown of По дороге к метро иди осторожнее: после дождя на улице скользко.
Questions & Answers about По дороге к метро иди осторожнее: после дождя на улице скользко.
По дороге is a set phrase meaning along the road / on the way.
Grammatically, по here takes the dative case, so дорога → дороге (dative singular). It’s very commonly used to mean “while going somewhere”: по дороге домой, по дороге на работу, etc.
К + dative means toward / to (the direction of) something: you’re going in the direction of the metro station.
В метро would mean into the metro / in the metro (subway system), i.e., you’re already entering it or inside it.
Метро is an indeclinable noun in Russian (it doesn’t change by case).
Even though к normally requires the dative, you still say к метро, not к метру.